Question

calculate the effective resistance between the points A and B in the circuit shown in the figure​

Answer 1

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

Effective Resistance between point A and B

$\color{darkblue}\underline{\underline{\sf Solution-}}$

We know that ⎯

Series Combination

$\color{violet}\bullet\underline{\boxed{\sf R_{eff}=R_1+R_2+R_3....so\:on}}$

Parallel Combination

$\color{violet}\bullet\underline{\boxed{\sf \dfrac{1}{R_{eff}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}....so\:on}}$

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Now We can see that ,

Upper 3 Resistance of 1Ω are in series Combination .

Therefore , in Series Combination

$\implies{\sf R'=1+1+1 }$

$\color{orange}\implies{\sf R'=3Ω}$

Lower 3 resistance of 2Ω are in Series Combination

therefore , in Series Combination

$\implies{\sf R=2+2+2 }$

$\color{orange}\implies{\sf R"=6Ω }$

Now ,

R' and R" and 2Ω Resistance are in parallel combination

therefore

$\implies{\sf \dfrac{1}{R"'}=\dfrac{1}{3}+\dfrac{1}{2}+\dfrac{1}{6}}$

$\implies{\sf \dfrac{1}{R"'}=\dfrac{12+18+6}{3×2×6}}$

$\color{orange}\implies{\sf R"'=1Ω }$

Now ,

1Ω R"' and 1Ω are in Series Combination

therefore

$\implies{\sf R_{eff}=1+1+1}$

$\color{red}\implies{\sf R_{eff}=3Ω }$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Effective Resistance between A and B is 3Ω

Answer 2

Answer:

3

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